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```STANDARD SUBSTANCES FOR THE CALIBRATION
OF VISCOMETERS

By Eugene C. Bingham and Richard F. Jackson

CONTENTS

Page

I. Introduction 59

II. Sucrose solutions 61

1 . Purification of sucrose . . . . 61

2 . Preparation of solutions 62

III. Measurement of viscosity 64

1. The viscometer 64

2. Viscosity formula 64

3. Calculation of constants in formula 65

4. Calculation of the pressure 65

5. Details in regard to instrument and measurements 69

IV. The Centipoise 72

V. Viscosity and fluidity of water 73

VI. Viscosity and fluidity of ethyl alcohol-water mixtures 76

VII. Viscosity of sucrose solutions 77

VIII. Summary 85

Appendixes 86

Appendix A. — Density in grams per milliliter of mixtures of ethyl alcohol

and water 86

Appendix B. — Density in grams per milliliter of sucrose solutions 86

I. INTRODUCTION

In making measurements of viscosity in absolute units it is
very desirable to have several substances available whose vis-
cosities are accurately known in order that the accuracy of the
method of measurement may be judged. Instruments whose
results are expressed in terms of merely arbitrary numbers do
not possess any advantage in this respect, since it is still neces-
sary that the numbers obtained by two different instruments of
the same type should agree, and in attaining this end the use
of two or more substances of known viscosity is obviously of

Water is naturally the most important substance for this pur-
pose since it can be so easily obtained in a pure condition and its
viscosities at different temperatures have been very carefully

59

60 Bulletin of the Bureau of Standards Voi.14

determined. But water is ill-suited for the calibration of the
short-capillary technical viscometer, since water is so very much
more fluid than most oils for which these instruments were
intended. In spite of the oft-repeated statement to the contrarv,
the viscosities of two substances are by no means directly pro-
portional to the times of flow of equal volumes through a given
capillary under the same head. The chief cause of this lack of
proportionality is the fact that the energy is not all expended in
overcoming viscous resistance, a part of it being used up in im-
parting kinetic energy to the fluid entering the capillary. Thus
in the flow of water through an Engler instrument only about 10
per cent ' of the total energy expended is used in overcoming
viscous resistance, the remaining 90 per cent being used in impart-
ing kinetic energy to the liquid. The presence of so large a kinetic
energy correction renders it manifestly desirable to have at hand
some substance of high viscosity which can easily be obtained in a
pure condition and whose viscosity is accurately known.

Castor oil and olive oil have been studied, but it has not been
determined to what extent the viscosity may vary with the con-
ditions of manufacture and exposure to light and air.

No pure hydrocarbon is readily available which possesses suffi-
ciently high molecular weight. Monoacid alcohols of high molec-
ular weight, like amyl alcohol, are not cheaply and easily obtained
in the pure and anhydrous condition. A mixture of 45 per cent
by volume of ethyl alcohol and water has a viscosity which is
almost exactly four times that of water at o° C. Since the viscos-
ity of ethyl alcohol-water mixtures passes through a maximum for
this concentration, the viscosity does not change rapidly with the
concentration, which is a marked advantage. The viscosities of
alcohol and water mixtures have been determined with care by
several observers.

When more viscous substances are desired, the poly-acid alco-
hols are available, and of these glycerol is perhaps the best for
the purpose. It is, however, hygroscopic and not readily obtain-
able in the pure anhydrous condition so that the preparation of
a solution of predetermined concentration offers some difficulty.

The sugars are valuable substances for the purpose. They are
not hygroscopic; they are cry stalliz able so that they may easily
be obtained in a very pure condition. The concentration of sucrose

1 Obtained by substituting the dimensions given in Ubbelohde's Tabellen zum Enqlerschen Viskosimeter,
p. 24, in our equation (;) assuming the viscosity of water at 20 to be 0.01005 and the time of flow to be 51
seconds.

jilsoT] Viscosity Standards 61

solutions may be determined by direct weighing of the constituents
or from the density of the solution, or by means of the polariscope.
Sucrose is very soluble in water, so that its solutions offer a wide
range of viscosities. There is no concentration of sucrose in water
which possesses the advantage of the alcoholic solution noted
above, whose viscosity is independent of the exact concentration;
hence it is necessary to guard the sucrose solutions against evapo-
ration. Fortunately the technique of handling sucrose solutions
has already been carefully worked out. 2

The viscosity of sucrose solutions has repeatedly been the
object of study, but the recent discovery 3 of important sources
of error in viscosity measurement which have hitherto remained
undetected makes it desirable that these solutions be the object
of still further research. Fortunately the data for water are suffi-
ciently complete so that the more important corrections thus far
recognized can all be made with sufficient certainty for our present
purposes.

II. SUCROSE SOLUTIONS

1. PURIFICATION OF SUCROSE

The sucrose used in preparing the solutions was purified by
crystallization from aqueous solution in the manner previously
described by Bates and Jackson. 4 Their procedure in outline was
as follows: The material, a quantity of good granulated cane sugar
of commerce, was dissolved in an equal weight of distilled water,
clarified with a small quantity of washed ''alumina cream/'
filtered and boiled in vacuo at a temperature of about 35 ° C until
a concentration of 80 per cent was reached. The supersaturated
sirup was seeded with a few crystals of sucrose and allowed to
crystallize while in continuous motion. The crystals were sepa-
rated from the mother liquor in a powerful centrifugal machine and
were washed with aqueous alcohol. The crystallization was
repeated until no evidence of impurity could be obtained.

The progress of the purification was studied and is described in
the paper referred to. They found that sucrose prepared by this
method contained less than 0.002 per cent of ash. The reducing
substances, aside from sucrose itself, were of the order of 0.00 1
per cent if present at all. The optical rotary power of the material
remained unchanged after fractional crystallization from aqueous

2 This Bulletin, 10, p. S3T, 1914-

* J. Am. Chem. Soc.,88, p. 27; 1916.

* This Bulletin, 13, p. 75, 1916; Scientific PaperNo. 268.

62 Bulletin of the Bureau of Standards Vol. 14

solution and after precipitation with ethyl and methyl alcohol.
The specific rotation of the substance in the concentration of the
normal 5 solution was found for X = 5892.5 A to be 66?529, or
slightly higher than the mean of the measurements of Tollens and
of Nasini and Villavecchia who found for it 66? 502. 6 The sugar
used in the present investigation was prepared from the same
source and possessed the same rotary power as that prepared by
Bates and Jackson.

2. PREPARATION OF SOLUTIONS

In preparing the solutions for the viscosity measurements the
constituents were weighed into a flask and the sugar dissolved.
The solution in general was not completely free from dust par-
ticles. The amount of dust was too small to be weighable, but by
accumulation in the capillary of the viscometer could readily have
affected the time of flow. The solution was consequently poured
on filters of hardened filter paper and repeatedly poured back to
remove shreds acquired from the paper. The clear solution was
finally poured through a funnel into a calibrated volumetric flask.

Three measurements of the concentrations of the solutions were
made, two of which depended upon the solution density and one
upon the rotary power.

number 0.02 ml apart. The interval between successive marks
could be estimated to one-tenth of one division. The original
solution was poured into the flask to some point on the scale, and
flask and solution immersed in the water of a thermostat. When
sufficient time had elapsed for the solution to assume the tempera-
ture of 2o?oo, its volume was observed. From these data the
density of the solution was calculated. Then by comparison with
the tables of the Kaiserliche Normal Eichungs Kommission, the
per cent composition of the solution was obtained.

The second measurement, made after the sample for viscometer
measurement was taken, consisted of determining the density of
the approximately normal solution taken for polarization. A
portion of the original solution was poured into another weighed
solution was taken to correspond to about 26 g of sucrose in 100

5 The normal concentration is 26 g in 100 ml of solution in accordance with the usage in sugar analysis.
9 This Bulletin, It, p. 125; 1916.

Bingham!
Jackson J

Viscosity Standards

63

ml. The sides of the flask were rinsed down into the solution and
the latter diluted nearly to the capacity of the flask. The tem-
perature was adjusted and the flask filled to the mark and weighed.
The third measurement consisted of a polarization of the approxi-
mately normal solution on a quartz-wedge saccharimeter. The
thoroughly mixed solution was poured into polariscope tubes of
known length and polarized at a fixed temperature. The read-
ing of the saccharimeter was controlled by comparison with
quartz plates No. 1 and No. 3, which are the primary standards
of this Bureau referred to and described in the paper by Bates
and Jackson. In determining the sugar value of these plates the
conversion factor 34?62o was used instead of the erroneous

34°657.

In addition to the solutions prepared from purified sucrose one
was prepared from a quantity of good granulated sugar of com-
merce in order to determine whether or not this generally avail-
able material would be suitable for standardization of instruments
of ordinary precision. The substance after filtration contained
but 0.012 per cent of ash. Its concentration was determined
from the density of the solution by the second method described
above, from its polarization, and from the reading of a standard-
ized hydrometer. Since the effect of the impurities upon the
fluidity was problematical, no attempt was made to apply correc-
tions for them. The mean value of the three determinations was
taken for the concentration. It is apparent that a calibrated
hydrometer gives a satisfactory determination of the concentra-
tion.

The summary of the analyses is given in Table 1 .

TABLE 1
Analytical Data on Sucrose Solutions

Percentage concentration by weight in vacuo

Solution

By density

of original

solution

By density
of solution
taken for
polarization

By polari-
zation

By stand-
ard hy-
drometer

Mean

No. 1

39.96
40.00
59.97
20. 003

40.01
39.97
59.93

39 99
39.99
59.93
20. 011
60.12

39 99

No. 2

39 99

No. 3

59 94

No. 4

20 007

No. 5

60.15

60.24

60 17

o Granulated sugar of commerce.

20172°— 17-

6 4

Fig. i. — The viscometer.

Bulletin oj the Bureau of Standards voi.14

III. MEASUREMENTS OF VISCOSITY

1. THE VISCOMETER

The viscometer used in this investigation
is shown in Fig. i. drawn to scale. The
method of making a measurement was as
follows: The clean and dry instrument was
rilled from H to .4 with the liquid to be
measured, the surplus liquid overflowing into
the trap at A. The liquid was introduced
by means of a pipette drawn out into a fine
tube. The left limb was connected with a
tank filled with air under a pressure which
could be measured on a water manometer,
the right limb already having been connected
with the air. The time which the meniscus
required in falling from B to D was taken as
the time of flow. The liquid was then in posi-
tion for an observation of the time of flow in
the opposite direction. When the tempera-
ture was raised, the volume was again ad-
justed by causing the surplus to run over
into the trap.

2. VISCOSITY FORMULA

Knowing the time of flow, t, the pres-
sure, p, and the two constants of the in-
strument, C and C, it became possible to
calculate the viscosity, 77, of the liquid for
the temperature of observation, using the
formula

v = Cpt-C' P jt (1)

The value of the density, p, does not need
to be accurately known, since it appears
only in the term which represents the
kinetic energy correction, which in our ex-
periments was purposely kept small in order
that the slight uncertainties in regard to the
value of the correction term might be ren-
dered nesrlible.

fJS&T] Viscosity Standards 65

The complete viscosity formula for the capillary tube method is

irgr^pt mnpv ( . ?

r? "87;(/+X)~87r/(/ + X) (2)

where v is the volume of flow, r is the radius, and / the length of
the capillary, X is a correction to be made to the length on account
of viscous resistance outside of the capillary and to the distortion
of the stream lines just within the entrance to the capillary.
According to all of the evidence at hand this correction is neg-
ligible when the capillary is very long in comparison with the
radius of the tube. The number of capillaries in series is repre-
sented by n, while misa constant whose value is being generally
accepted to be about 1.12. 7

3. CALCULATION OF CONSTANTS IN FORMULA

From the approximate dimensions ^ = 4.00 and / = 7.50 we can
calculate the value of C

„, mnV , , .

c = 87r = °-° 2376 (3)

Observing the rate of flow of pure water at 20 C under a given
pressure, and taking the absolute viscosity of water at this tem-
perature to be 0.01005, we may calculate the value of C

4. CALCULATION OF THE PRESSURE

The pressure used in the above formulas is expressed in grams
per square centimeter. It is obtained as follows : If the height read
on the manometer scale — corrected for scale error, if necessary —
is h , Fig. 2, and the density of the liquid in the manometer is p ,
then the pressure is h p Q . But this pressure is subject to several
corrections which may be small but must be taken into considera-
tion. (1) The correction for buoyancy of the air is — h p air. (2)
The air in the closed limb of the manometer is under pressure and
is therefore denser than the air outside. If the middle of the bulbs
of the viscometer were at the level of the middle of the manometer

the correction for this cause would amount to — - p B ir — ™ (3)

2 1033

7 Zs. physik. Chem., 80, p. 681; 1912.

66

Bulletin of the Bureau of Sta?idards

Voi.14

If, however, the middle point of the manometer is at a distance h'
below the middle of the viscometer, there is a further correction

-h'p

air

I033

• (4) There is a further correction for the hydrostatic

head within the viscometer, arising from the fact that it is impos-
sible to construct an instrument in which the two bulbs are of
exactly the same shape and size or at the same height. If the

Fig. 2. — Diagram illustrating the method of estimating the pressure used in a viscosity

determination.

hydrostatic head is h u Fig. 2, obtained as will be described later,
the pressure correction w r ill be h x p and this may be either negative
or positive, dependent upon the limb to which the pressure is being
admitted; that is, whether the left limb is emptying or filling.

Making these corrections we have for the assumed constant
pressure

h

po = h p — h pi ir

ho 2

2^66 *l'± &1 *tr —

±h l p

(5)

Bingkaml
Jackson J

Viscosity Standards

67

We have calculated Tables 2 and 3 which simplify the use of the
above formula, and cause the formula to take the form

p = h ±h lP -K±L (6) 8

In this formula h is the height in centimeters of the water column
in the manometer, k ± is the hydrostatic head, and p the density
of the liquid within the viscometer, L is the correction for the
difference of level between viscometer and manometer. This
correction may usually be made negligible in the construction of the
apparatus, but if necessary, the corrections corresponding to
different values of h' and h may be obtained from Table 2. Table
3 contains the values of K, including the corrections for tempera-
ture, buoyancy, etc., for the different temperatures and pressures.
A single example will serve to show the method of using the
tables. In our viscometer L was negligible, but the hydrostatic
head was /^ =0.2 cm, the right bulb of the viscometer being higher
than the left, so that, for a 40 per cent sugar solution at 20 C,
p = i.i76, and at a pressure read on the manometer of & = 269.5
cm at 23 C, the correction is (0.77+0.22 +0.03) +0.24 = 1.3 cm 9
when the pressure is on the left limb, or (0.77+0.22+0.03) —
0.24 = 0.8 cm when the pressure is on the right limb of the
viscometer.

TABLE 2
Values of L

h' in centimeters

h in centimeters

100

200

300

50

0.01
.01
.03
.04

0.01
.03
.05
.08

0.02

100 ;

.04

200

.08

300

.11

(5) The applied pressure p is not necessarily the true average
pressure to be used in the viscosity formula, hence a further cor-
rection may be necessary. Bingham, Schlesinger, and Coleman 9 \
have shown that if the bulbs of the viscometer were cylindrical
in shape and of the height h, the true average pressure p, obtained
by integration, would be

0.8686&P

P =

loe h±h£

(7)

AoVair

8 In obtaining (6) from (5) K=ho— hoPo+hop*ii+——7jr'

9 The figures within the parenthesis are the interpolated value of . K
8 » J. Amer. Chem. Soc., 37, p. 27; 1916.

68

Bulletin of the Bureau of Standards

Vol. 14

but the difference between p and p becomes less than 0.05 per
cent — that is, negligible for ordinary purposes — when the value of
p becomes as great as 30 times that of Up. They have shown
how to obtain the value of h when this correction is not negligible
and the bulbs of the viscometer are not true c vlinders.

TABLE 3
Values of K

Temperature,

C

10

20

N

40

50

60

70

80

M

100

200

300

5

0.013
.016
.017
.018
.019
.020
.022
.023
.025
.027
.029
.031
.033
.035
.037
.040
.042
.045
.048
.050
.053
.056
.059
.062
.066
.069

0.025
.030
.032
.035
.037
.040
.043
.ON
.049
.053
.057
.060
.065
.069
.074
.079
.084
.089
.094
.100
.105
.111
.117
.124
.130
.137

0.039
.045
.050
.053
.057
.061
.065
.070
.075
.080
.086
.092
.098
.105
.112
.119
.127
.135
.143
.151
.160
.169
.178
.188
.197
.207

0.053
.064
.068
.072
.077
.082
.088
.094
.101
.108
.116
.124
.132
.141
.151
.160
.170
.181
.191
.202
.214
.226
.239
.251
.264
.277

0.066
.078
.083
.089
.095
.102
.110
.118
.126
.135
.144
.154
.165
.176
.188
.200
.212
.225
.239
.253
.268
.283
.298
.314
.330
.346

0.079
.095
.101
.106
.115
.123
.131
.140
.150
.161
.173
.185
.198
.211
.225
.240
.255
.270
.286
.303
.321
.339
.357
.376
.395
.415

0.094
.112
.119
.126
.135
.144
.154
.165
.176

.us

.203
.217
.232
.247
.264
.281
.298
.316
.335
.355
.375
.396
.417
.439
.462
.485

0.108
.129
.137
.145
.155
.165
.177
.189
.203
.217
.233
.249
.265
.282
.301
.321
.341
.362
.383
.405
.429
.453
.478
.503
.529
.555

a 122

.145
.154
.163
.175
.187
.199
.212
.228
.245
.262
.280
.299
.319
.341
.363
.385
.408
.432
.458
.484
.511
.538
.567
.595
.625

0.136
.162
.172
.183
.195
.208
.222
.238
.255
.273
.292
.312
.333
.355
.379
.403
.428
.454
.481
.509
.538
.568
.599
.630
.662
.695

0.285
.337
.357
.379
.403
.429
.457
.439
.523
.559
.597
.637
.679
.723
.770
.819
.869
.921
.975
1.031
1.089
1.149
1.210
1.273
1.337
1.403

0.482

10

.533

11

.563

12

.596

13

.632

14

.671

15

.713

16

.761

17

.812

18

.866

19

.923

2*3

.983

21

1.046

22

1.113

23

1.184

24

1.256

25

1.331

26

1.409

27

1.490

28

1.574

29

1.661

30

1.751

31

1.842

32

33

34

1.937
2.033
2.132

To obtain the hydrostatic head h x , we determine the times of
flow f, and /, for some substance, such as water at 20 C, for the
right and left limbs of the instrument, respectively, with a given
pressure, which is p u corrected except for the hydrostatic head.
We have the equations

and

*♦*,.*§*
*-*,-*£&

jZg™] Viscosity Standards 69

hence

In obtaining h x it is sufficient to use the approximate value of C,
obtained by using p 1 in place of p in equation 4.

5. DETAILS IN REGARD TO INSTRUMENT AND MEASUREMENTS

The bulbs of the viscometer were made as short as practicable
in order that the difference between the applied pressure and the
true average pressure might be a minimum. The distance between
the marks B and D was 3.0 cm.

The bulbs were made conical in shape in order to obtain the
necessary volume while avoiding nearly horizontal surfaces which
might cause faulty drainage. Drainage troubles were further
obviated by having the part of the instrument directly above the
point B in Fig. 1, similar in shape to the part above the point D.
By always reading the volume of flow on the left limb, irrespective
of whether the direction of flow is from left to right or vice versa,
we measure the time of flow of the volume which the bulb C
delivers in the former case but of the capacity of the bulb in the
latter case. Thus any differences in the viscosity calculated from
the times of filling and emptying of this bulb may serve as a test
of the completeness of the drainage. A further test can of course
be made by making observations of the time of flow at different
pressures. 10

The capillary tube was cut off squarely and sealed into the
instrument so as to avoid a trumpet-shaped opening in order that
there may be no doubt about the maximum value of the kinetic
energy correction being applicable.

In order to prove that the corrections made are trustworthy, a
series of observations were made on water at 25 ° C, using a con-
siderable range of pressures. Table 4 shows that the calculated
viscosity is satisfactorily constant.

10 By using an instrument similar to the one described in this Bulletin, 12, Scientific Paper No. 278.
p. 309 (1916), all possibility of error due to bad drainage can be obviated, but in the present investiga-
tion that type of instrument is far less convenient than the one adopted and fortunately its use is
unnecessary.

7o

Bulletin of the Bureau of Standards

Vol. 14

TABLE 4

Viscosity of Water at 25° C Calculated from the Constants Obtained from Observations
on the Rate of Flow of Water at 20° C, Assuming the Viscosity at this Temperature to
be 0.01005 (C=0.000000 14307 and C'=0.02376)

Limb

R
L
R
L
R
L
R
L
R
L
R
L

t

P

Sees.

g/cm J

570.9

110.04

572.9

109.65

570.6

110.04

572.9

109. 65

571.3

110.04

572.4

109.65

819.2

76.76

821.2

76.37

818.2

76.81

820.6

76.42

399.4

157. 56

400.6

157. 19

g/cm J
109.53
109.14
109.53
109.14
109.53
109.14
76.51
76.12
76.56
76.17
156. 53
156.16

0.008946
.008946
.008942
.008946
.008952
.008938
.008968
.008944
.008963
.008943
.008944
.008950

Limb

Sees.
399.6
400.2
306.5
307.6
306.5
308.1
274.8
276.8
274.4
274.8
273.4
275.1

g/cm»

157. 59
157. 22
205. 43
205.04
205.44
205. 05
229.64

228. 08

229. 48
229. 58
230.45
229. 72

g/cm»

156.56
156.19
203. 67
203.28
203.68
203.29
227. 45
225. 92
227. 29

227. 39

228. 24
227. 53

0. 008951
. 008943
.008931
.008946
.008932
.008961
.008943
.008947
.008923
.008940
.008928
. 008955

In the above table, as well as in succeeding tables, we have
given not merely the true average pressure p, but also the part of
this pressure P, which is used up solely in overcoming viscous
resistance. It is calculated by means of the formula

whence we have that

l = Cpt-C'p/t = CPt

P = p-

a 2

(9)

The object in recording both p and P is in order to afford a
measure of the kinetic energy correction.

The viscometer was attached to a brass frame which fitted in
grooves on the side of the bath shown in Fig. 3, so that the vis-
cometer was necessarily always in the same position. A part of
the viscometer always projected above the bath, so that any
vapor rising from the solution would tend to condense and run
back. It may be remarked that the experiment was tried of
repeating a measurement after heating a solution for several
hours and then cooling, but without noteworthy effect.

The temperature was read by means of a telescope to one one-
been calibrated at the Reichsanstalt, it was unnecessary to rede-
termine its corrections, but its ice point was determined before
and after the investigation. At the two highest temperatures
used a part of the stem of the thermometer was exposed, for which

Bingkaml
Jackson *

Viscosity Standards

71

C-'v

Fig. 3. — Detail of bath and frame with viscometer in position

7- Bulletin of the Bureau of Standards Vot.u

The time was measured on an Agassiz stop watch which had
been tested by this Bureau and given a rating of 56.2 in class A. u
It was losing at the rate of a minute in a month during the time
of the experiments.

IV. THE CENTIPOISE

It has been common practice to record viscosities in other
than absolute units. There are at least three reasons for using
specific viscosities rather than absolute viscosities. Absolute
viscosities are often inconveniently small fractions, necessitating
the use of many ciphers. We naturally compare the viscosity of
any liquid with that of water, which is usually used as the stand-
ard, hence the specific viscosity makes an immediate impression
upon the mind which the absolute viscosity does not until after
considerable practice. Finally, the so-called specific viscosi-
ties are often arbitral*}- numbers which are not reducible, or at
least not easily reducible, to absolute units. Thus in the use of
most technical instruments such as those of Engler and Saybolt,
the so-called viscosities are recorded in terms of arbitrary num-
bers known as Engler degrees or Saybolt seconds, respectively.
These numbers are far from being proportional to the absolute
viscosity, and the absolute viscosity is not in any way calculable
without a supplementary determination of the density, the
determination of which is often omitted.

It is quite evident that in studying the relation of viscosity to
other properties it is the true absolute viscosity that is desired.
This is the strongest possible argument in favor of giving up the
use of purely arbitrary numbers and expressing all results in
absolute measure. Moreover, whether the specific viscosities
are reducible to absolute units or not it is awkward to make com-
parison between specific viscosities based upon different standards.
Thus, when one worker uses water at o° C as his standard it is
not easy to compare his work with that of another worker who
used as a standard water at 25 C. or either of these with results
expressed in absolute units.

When two liquids having the same viscosity as measured on one
instrument are measured in a different type of viscometer it has
often been noted that the two liquids have quite different apparent
specific viscosities. This arises from the fact that, in calculating
the specific viscosity, important corrections are not taken into
account which affect the two instruments differently. Thus, it is

u Circular No. 51. Bureau of Standards.

/ST] Viscosity Standards 73

an objection to the use of specific viscosities that it has heretofore
encouraged slovenly thinking in regard to the subject of viscosity
measurement.

These views as to the relative merits of specific or absolute units
are not as irreconcilable as may seem at first. It can probably be
agreed that all viscosity measurements should be made under con-
ditions such that the results can be expressed in absolute units. It
is further desirable that, if specific viscosities be used, the same sub-
stance be taken as standard by all and that the absolute viscosity
of the standard be definitely agreed upon, just as there is general
agreement in the acceptance of atomic weights. If the suggestion
of Deeley and Parr 12 is accepted, and the absolute cgs unit of vis-
cosity be known as the " poise," then it is convenient to use the
submultiple of this unit, which is one-hundredth as large, and
which may therefore properly be called the centipoise (cp) . It so
happens that the centipoise is almost exactly the viscosity of water
at 20 C, hence viscosities expressed as centipoises have the added
advantage of being at the same time the specific viscosity of the
substance referred to water as standard at almost exactly 20 C.

V. VISCOSITY AND FLUIDITY OF WATER

Previous determinations of the absolute viscosity of water and
other substances have neglected to take into account the possible
difference between the mean applied pressure and the true average
pressure. It has therefore seemed desirable to go over the data
available and make the correction where necessary and practicable.

Thorpe and Rodger 13 calculated their viscosities on the assump-
tion that m = 1. 00 instead of the more generally accepted value 14
w = i.i2. They also calculated the viscosity of water from the
observations of Poiseuille, 15 Sprung, 16 and Slotte 17 on the same
assumption, hence it has seemed desirable to go over this data
and make the needed correction. The error in the true average
pressure and the error in the value of m are both in the same
direction, both tending to make the substance appear to be more
viscous than it really is. In a few instances the error amounts
to as much as 0.3 per cent.

In arriving at the most probable values for the viscosity of
water, it is important to observe that Poiseuille is usually credited

12 Phil. Mag. [6], 26, p. 85; 1913.

1S Phil. Trans., 185A, p. 397; 1894.

"Seep. 6 S .

15 Mem. present, par divers Savants a l'academie Roy. des Sciences de l'lnst. de France, 9, p. 4.53; 1840.

18 Pogg. Ann., 159, p. 1; 1876.

" Wied. Ann., 20, p. 357; i88ju

74

Bulletin oj the Bureau of Standards

1W. 14

with one series of observations from o° to 45 °, whereas he actually
made observations over this range of temperatures with four
different capillaries, and as there is no reason for supposing that
his observations were any less accurate than were those of his
successors, we have recalculated his data entire.

Hosking 18 does not give sufficient data to permit a recalculation
to be made, but as he adjusted the values of m and X in such a way
as to get concordant values of viscosities at different pressures, it
seems proper to include his values as they are recorded by him.

TABLE 5
Viscosity of Water in Centipoises as Determined by Different Observers

Tempera-
ture, C C

Poteeuille

|

Thorpe Bing-
<?T»mnff Slotte ' and Hosk- ham

Aver-

Calcu-
lated by

A* C D' E

Rod- ing and
ger Whiter

1

age

for-
mula

1.7900

1.7944

1.777
1.5089
1.2995
1.1334
.9978
.8947
.8183

1.807
1.523
1.313
1.143
1.007
.895
.802

1.7766
1.5083
1.3014
1. 1324
1.0005
.8900
.7965

1.7928
1.522
1. 3105

1.7960
1. 5241
1.3002

1.7887
1.5155
1.3061
1.1406
1.0046
.8941
.8019

1. 7921

5

1. 5108
1.3045
1.1385
1.0028
.8900
.7958
.7154
.6466
.5867

1. 5137
1.3078
1.1464
1.0073
.8964
.8016
.7194
.6523
.5934

1.5143
1.3088
1.1465
1.0063
.8966
.8011
.7190
.6508
.5937

1. 5142
1.3088
1.1456
1.0087
.8973
.8027

1.5188

10

1.3077

15

1.142 ! 1.1373
1.006 1.0054
. 8S26 . 8940

1. 1404

20

1.0050

25

.8937

30

.800

.7991

.8007

35

. 7207 I . 7216
. 6531 ! . 6558
.5932 .6001

.723 .7190
. 656 . 6525
.601 .5959
.552 .5464
.509 .5044
. 471 . 4676

.724

.657

.600

.5500

.508

.469

.436

.406

.380

.356

.335

.316

.300

.7223
.6557
.5984
.5491

. 7205 - 7225

40

.6533
.5958

.5497

.6560

45

.5988

50

.5512

.5494

55

. 5073 - 5072

.5064

60

.4728
.4362
.4069
.3794
.3558
.3337
.3133
.2983

.4701
.4359
.4062
.3794
.3556
.3341
.3146
.2981
.2821

.4688

65

.437

.4343

.4355

70

. MS
.380
.356
.334
.315

.4048
.3782
.3547
.3336
.3140
.2970
.2814

.4061

75

.3799

80

.3565

.3355

90

.3165

,5

.297
.281

.2994

100

. 2838

° Zs. physik. Chem.. 83, p. 641; 1913.

In next to the last column of Table 5 are given the averages of
the values of the different observers. In the last column are given
the values given by the formula

B

t = A(<P-D)-C-

6-rD

(10)

which has been shown to be capable of expressing quite accurately
the fluidity of liquids over a range of temperature, A , B, C, and D
being arbitrary constants, and <f> being the fluidity in cgs units. We

Phil. Mag. [c], 17, p. 502. 1909; 18, p. :6c. 1909.

Bingham!
Jackson J

Viscosity Standards

75

have taken A =0.23275, 5 = 8676.8, C = 8.435, and D = i2o. The
calculated values are for the most part very close to the average
observed values. This is particularly true between 5 and 8o°.
It seems probable, therefore, that in taking 1.005 C P as tne vis-
cosity of water at 20 C all of the figures are significant.

It is often desirable to know the viscosity of water at other than
the 5 -degree intervals given above, hence we have calculated the
fluidity and viscosity of water for every degree between o° and
ioo°, using equation (10) in the form

= 2.i482{(^-8.435)+V8o78.4 + (^-8. 4 35) 2 }-i2o

TABLE 6

Fluidity and Viscosity of Water Calculated by Formula for Every Degree Between 0°

and 100° C

Temperature,
°C

Flu-
idity

Vis-
cosity
incp

Temperature,
°C

Flu-
idity

Vis-
cosity
incp

1

Temperature,
°C

Flu-
idity

Vis-
cosity
incp

55.80
57.76
59.78
61.76
63.80
65.84
67.90
70.01
72.15
74.28
76.47
78.66
80.89
83.14
85.40
87.69
90.00
92.35
94.71
97.10
99.50
100.00
101.94
104. 40
106. 86
109. 38
111.91
114. 45
117. 03
119. 62
122. 25
124. 89
127. 54
130. 22

1. 7921
1. 7313
1. 6728
1. 6191
1. 5674
1. 5188
1. 4728
1. 4284
1. 3860
1. 3462
1. 3077
1. 2713
1. 2363
1. 2028
1. 1709
1. 1404
1.1111
1. 0828
1. 0559
1.0299
1. 0050
1.0000
.9810
.9579
.9358
.9142
.8937
.8737
.8545
.8360
.8180
.8007
.7840
.7679

33

132. 93
135. 66
138.40
141. 15
143. 95
146. 76
149. 60
152. 45
155. 30
158. 20
161. 11
164. 02
167. 00
169. 97
172. 95
175. 95
178. 95
182. 00
185. 05
188.14
191. 23
194. 34
197. 45
200. 62
203. 78
206. 95
210. 13
213. 33
216. 54
219. 80
223. 07
226. 34
229.64
232. 94

0. 7523
.7371
.7225
.7085
.6947
.6814
.6685
.6560
.6439
.6321
.6207
.6097
.5988
.5883
.5782
.5683
.5588
.5494
.5404
.5315
.5229
.5146
.5064
.4985
.4907
.4832
.4759
.4688
.4618
.4550
.4483
.4418
.4355
.4293

67

236. 25
239. 57
242. 91
246. 26
249. 63
253. 02
256. 42
259. 82
263. 25
266. 67

270. 12
273. 57
277. 04
280. 53
284. 03
287. 53
291. 03
294. 54
298. 06
301. 63
305. 21
308. 78
312. 35
315.92
319. 53

323. 13
326. 74
330. 38
334. 01
337. 65
341. 30
344. 96
348. 63
352. 30

0. 4233

1...;

34

68

.4174

2

35

69

.4117

3

36

70

.4061

4

37

71

.4006

5

38

72

.3952

6

39

73

.3900

7

40

74

.3849

8

41

75

.3799

9

42

76

.3750

10

43

77

.3702

11

44

78

.3655

12

45

79

.3610

13

46

80

.3565

14

47

81

.3521

15

48

82

.3478

16

49

83

.3436

17

50

84

.3395

18

51 .

85

.3355

19

52

86

.3315

20

53

87

.3276

20.20

54

88

.3239

21

55

89

.3202

22

56

90

.3165

23

57

91

.3130

24

58

92

.3095

25

59

93

.3060

26

60

94

.3027

27

61

95 ..

.2994

28

62

96

.2962

29

63

97

.2930

30

64

98

.2899

31

65

99

.2868

32

66

100

.2838

76

Bulletin of the Bureau oj Standards

Vol. 14

VI. VISCOSITY AND FLUIDITY OF ETHYL ALCOHOL- WATER

MIXTURES

It was stated above that ethyl alcohol-water mixtures possess
certain advantages for the purpose of testing viscometers. They
have already been used successfully for this purpose by AYinslow
H. Herschel, of this Bureau.

The fluidities of ethyl alcohol-water mixtures have already been
determined by various observers, the data being brought together
in a paper by Bingham, White, Thomas, and Cadwell. 19 The
older data is subject to some uncertainty on account of various
circumstances, hence in getting the average some system of
weighting seemed necessary. In obtaining the average values
given in Tables 7 and S the data of Bingham and Thomas 19 was
given a weight of three, that of Xoack 2n of two, and that of
Traube,- 1 Pagliani, and Batelli," and Stephan :3 of one.

TABLE 7
Fluidity of Alcohol-Water Mixtures

Tem-
perature,

Weight, percentage of ethyl alcohol

II

:■:

30

GO 70 80

?■:

Volume, percentage of ethyl alcohol at 25° C

12.36 24.1

C.

5..
10..
15..
20..
25..
30..
35..
40..

45 167.0

50 182.0

55 1 197.4

60 213.3

65 1 229.6

70..

55.8
65.8
76.5
87.7
99.5
111.9
124.9
138.4
152.4

. 246.3

75 263.2

80 280.5

30.2

38.8

45.9

55.8

65.0

75.6

86.2

99.4

110.2

123.2

136.3

150.9

164.3

180.5

194.5

210.2

232.7

18.8

24.6

31.6

38.2

45.8

55.1

64.4

75.1

86.2

98.5

110.2

122.9

135.8

150.1

164.5

178.8

198.1

35.23

14.4

18.9

24.7

30.7

36.9

45.9

53.4

63.3

73.1

84.1

95.2

107.6

119.9

133.0

146.4

160.3

176.4

^5.83 50.94 55.93

65. 56 I 74. 80

13.8
17.8

22.8

28.4

34.7

42.5

50.0

58.6

67.9

77.9

89.0

100.7

113.0

125.3

138.0

151.5

167.1

14.0

17.9

22.8

28.3

34.4

42.5

49.4

58.3

67.5

77.6

88.3

100.2

112.0

124.7

137.5

150.8

166.5

14.4

18.2
23.0
23.5

41.9

49.5 .

57.7

66.9

76.5

87.1

98.4

110.3

122.6

135.2

148.9

164.1

15.2*

19.0

23.9

29.1

34.8

41.7

49.6

58.0

66.7

77.3

86.6

98.0

109.5

122.3

135.1

148.7

163.5

17.4
21.6
26.5
31.8
37.4
44.6
51.9
60.1
69.1
78.7
85.7
100.3

no.8 ;

124.1
137.2
150.8
165.7

21.0

25.6

30.6

36.1

42.2

49.1

56.6

65.4

74.4

84.1

94.2

106.0

116.8

130.6

143.9

157.1

92.01 100

27.1

32.0

36.9

43.3

49.8

57.2

65.3

73.8

83.1

92.5

103.3

115.3

126.7

140.7

153.9

166.6

36.6

43.3

47.6

55.5

62.1

70.2

78.2

87.2

96.6

106.5

117.9

130.8

142.1

156.0

169.9

183.0

100

56.4

61.6

68.2

75.1

83.3

91.2

99.7

109.4

119.9

130.8

142.5

155.2

168.9

181.5

198.6

212.5

" Zs. physik. Chem., 83, p. 644; 1913.

M Wied. Ann.. 27, p. 289; 18S6.

■ Bcr. d. deutsch. chem. Gesell., 19, p. S71; 1886.

*= Atti. d. R. Ace. di Torino, 20, p. 845; 1885.

» Wien. Ber., 48 (aa). p. 495; 1862.

Bingkaml
Jackson J

Viscosity Standards

TABLE 8
Viscosity in Centipoises of Alcohol-Water Mixtures

77

Weight, percentage of ethyl alcohol

Tem-
perature,

°C

10

20

30

39

40

1
45 1 50

!

60

70

80

90

100

Volume, percentage of ethyl alcohol at 25° C

12.36

24.09

35.23

44.92

45.83

50.94

55.93

65.56

74.80

83.59

92.01

100

5

10

15

20

25

30

35

40

«

50

55

60

65

70

75

80

1.792
1.519
1.308
1.140
1.005
.894
.801
.722
.656
.599
.549
.507
.469
.436
.406
.380
.356

3.311
2.577
2.179
1.792
1.538
1. 323
1.160
1.006
.907
.812
.734
.663
.609
.554
.514
.476
.430

5.319
4.065
3.165
2.618
2.183
1.815
1.553
1.332
1.160
1.015
.907
.814
.736
.666
.608
.559
.505

6.94
5.29
4.05
3.26
2.71
2.18
1.87
1.58
1.368
1.189
1.050
.929
.834
.752
.683
.624
.567

7.25
5.62
4.39
3.52
2.88
2.35
2.00
1.71
1.473
1.284
1.124
.993
.885
.798
.725
.660
.598

7.14
5.59
4.39
3.53
2.91
2.35
2.02
1.72
1.482
1.289
1.132
.998
.893
.802
.727
.663
.601

6.94

5.50

4.35

3.51

2.88

2.39

2.02

1.73

1.495

1.307

1.148

1.016

.907

.816

.740

.672

.609

6.58
5.26
4.18
3.44
2.87
2.40
2.02
1.72
1.499
1.294
1.155
1.020
.913
.818
.740
.672
.612

5.75
4.63
3.77
3.14
2.67
2.24
1.93
1.66
1.447
1.271
1.127
.997
.902
.806
.729
.663
.604

4.762

3.906

3.268

2.770

2.370

2.037

1.767

1.529

1. 344

1.189

1.062

.943

.856

.766

.695

.636

3.690

3.125

2.710

2.309

2, 008

1.748

1. 531

1.355

1.203

1.081

.968

.867

.789

.711

.650

.600

2.732

2.309

2.101

1.802

1.610

1.424

1.279

1.147

1.035

.939

.848

.764

.704

.641

.589

.546

1.773

1.623

1.466

1.332

1.200

1.096

1.003

.914

.834

.764

.702

.644

.592

.551

.504

.471

VII. VISCOSITY OF SUCROSE SOLUTIONS

The first sucrose solution used was 39.99 per cent sucrose by
weight in vacuo. The results obtained are given in Table 9 and
plotted in Figs. 4 and 5. The first column shows whether the left
or the right limb was emptying, the second column gives the cor-
rected time of flow in seconds, the third column gives the corrected
pressure, while the fourth column gives the pressure used up in
overcoming the viscous resistance, and the fifth column gives the
fluidity calculated for the measured temperature given in the
sixth column. In the last column the temperatures 24 are calcu-
lated corresponding to these fluidities, using the formula

14^8.6
t = (<p + 20) 0.597 - -j~^ + 38.24

The agreement between the observed and calculated values is
good.

Were the fluidity concentration curves linear they would
follow the dotted lines. That the observed curves depart so

u The temperatures are calculated instead of fluidities purely for the sake of convenience in the use of
the formula.

78

Bulletin of the Bureau of Standards

Vol. t 4

K

51

3 50

1

/

FLUIDITY-TEMPERATURE RE-
LATION FOR VARIOUS CON-
CENTRATIONS OF SUCROSE.

/

/

/

/

j\

f

300

/

}

t

/

/

/

150

/

/

/

1/

200

\$/

/

/

/

A

/

/

/

/

r

/

150

/

/

f

/

/

t

/

/

/

/

/

4

V

/

>

/

100

/

y

/

j

/

/

/

/

*

/

/

J

/

/

'

/

/

/

/

y

/

s>

r

50

T"

/

r-

&

s

y

Y

p^

0+

n

o ^o o 40°

TEMPERATURE

60'

80°

100°C

FlG. 4. — Showing the relation between fluidity and temperature for solutions of various

sucrose content

Bingham!
Jackson J

Viscosity Standards

79

widely from the linear is an indication of the chemical hydration

of the sugar.

TABLE 9

Fluidity of a 39.99 Per Cent Sucrose Solution at Various Temperatures

Limb

Time.t

Pressure,
P

Pressure,
P

Fluidity,

Tempera-
ture
measured

Tempera-
ture
calculated

L

Seconds

3, 487. 8

3,437.1

2,236.4

2, 199. 7

1, 486. 7

1, 477. 8

1, 266. 1

1,250.4

918.1

908.4

730.6

747.3

543. 3

545.8

437.1

437.3

363.7

363.2

306.3

307.3

257.8

257.2

290. 65

292. 97
289. 15

293. 43

291. 94
293. 19
286. 44
289. 92
286. 39
289. 24
288. 74
289. 17

283. 34

284. 76

284. 33

285. 07
282. 29
283.14
280. 13
279. 58

282. 76

283. 08

290. 65

292. 97
289. 11

293. 39

291. 85

293. 10
286. 32
289. 80
286. 16
289. 01
288. 40
288. 83

282. 71
284. 13

283. 34

284. 08

280. 85

281. 70

278. 11
277. 56
279. 93
280. 25

6.89
6.94
10.81
10.83
16.11
16.14
19.28
19.29
26.58
26.60
35.09
35.21
45.09
45.07
56.18
56.26
68.43
68.32
82.05
81.95
96.86
96.97

0.32
.46
9.96
9.96
19.98
19.98
24.99
24.99
35.00
35.00
45.00
45.00
54.99
54.99
64.96
64.96
74.94
74.94
85.03
85.03
95.30
95.30

°C
0.81

R

.94

L

9.94

R

9.98

L

19.96

R

20.00

L

25.07

R

25.08

L

35.17

R

35.19

L

44.92

R

45.14

L

55.00

R

54.98

L

64.83

R

64.91

L

74.76

R

74.69

L

85.39

R

84.99

L

95.69

R

95.77

The values of the fluidity given above do not agree with the
values obtained by other observers, as will be shown later, hence
the viscometer was tested with pure water and another series of
measurements were made with an entirely new solution, which,
however, happened to have the same concentration as the former,
viz, 39.99 per cent by weight.

TABLE 10
Fluidity of a Second 39.99 Per Cent Sucrose Solution at Various Temperatures

Limb

Time, t

Pressure,
P

Pressure,
P

Fluidity,

Tempera-
ture
observed

Tempera-
ture
calculated

L

Seconds

2,024.4

1, 256. 4

1,232.4

1,045.3

1,039.8

770.6

768.4

594.0

593.1

257. 97
288. 16
293. 15

293. 24

294. 43

295. 00
295. 41
294. 30
294.63

257. 92
288. 04
293. 02
293. 04
294.27
294.65
295. 10
293.73
294.10

13.39
19.31
19.36
22.82
22.84
30.78
30.82
40.06
40.07

°C

14.97
24.99
24.99
30.00
30.00
40.00
40.00
50.00
50.00

°C
15.10

L

25. 12

R

25.18

L

30.10

R

30.24

L

40.23

R

40.27

L

50.14

R

50.15

8o

Bulletin of the Bureau of Standards

voi.14

The second sample gave values which correspond very well with
the former values, hence we have additional reason for confidence
in the reliability of our values. It should be noted in this con-
nection that Bingham, Schlesinger, and A. B. Coleman, 25 using a
viscometer of different construction, have already noted that the
observations of Hosking on sugar solutions may be in error. This
was confirmed by the measurements of C. Coleman. 25

^

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AT VARIOUS TEMPERATURES.

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Fig. 5. — Showing relation between fluidity and sucrose content at various temperatures

Having found an appreciable difference between our own values
and those of other observers, it seemed desirable to measure the
fluidity of a 20 per cent solution, the concentration actually
obtained being 20.007 P er cent. The fluidities are given in Table
1 1 . The last observation recorded in the table was made several
hours after the preceding observation, when the solution had cooled
down from the high temperature. The fluidities are again con-
siderably smaller than the values found by Hosking.

»Loc. cit.

Bingkaml
Jackson J

Viscosity Standards

81

TABLE 11
Fluidity of a 20.007 Per Cent Sucrose Solution at Various Temperatures

Limb

Time, t

Pressure,
P

Pressure,
P

Fluidity,

Tempera-
ture

L

Seconds
899.1
897.0
643.4
644.2
414.7
415.5
263.4
261,4
324.5
324.3
217.8
215.8
201.3
200.5
213.1
212.4
248.4
247.4
1, 783. 8

290 43
290. 86
289. 26
288. 77
288.42

287. 77
288. 91

288. 89
288. 52

288. 71
287. 93

289. 86
262. 51
262.86
212. 40
212. 84
157. 68
158. 13

76.92

290. 21
290.64
288. 83
288. 34
287. 38
286. 73
286.35
286. 29

286. 82

287. 01
284. 20
286. 06
258. 17
258. 48
208. 55
208.96
154. 86
155. 29

76.86

26.79
26.81
37.61
37.63
58.65
58.67
75.10
75.09

°C

0.44

R

.44

L

9.96

R

9.96

L

24.99

R

24.99

L

35.00

R

35.00

L

45.00

R

93.40

112. 92
113. 22
134. 50
134. 89
157. 28
157. 48
181. 72

181. 93
50.98

45.00

L

54.99

R

54.99

L

64.96

R

64.96

L

74.94

R

74.94

L

85.03

R

85.03

L

19.98

Table 12 contains the results of measurements of the fluidity
of a solution which contained 59.94 per cent sucrose by weight.
This concentration has not been measured over a range of tem-
peratures by previous observers.

TABLE 12
Fluidity of a 59.94 Per Cent Sucrose Solution at Various Temperatures

Limb

Time, t

Pres-
sure, p

Pres-
sure, P

Fluidity,

Tem-
perature
observed

Tem-
perature
calculated

L

Seconds

26, 023

10, 310
6,222
4,029
2, 736. 6
1,957.2
1, 392.
1,111.3
870.6
1, 508. 4

295. 87

296. 61
295. 76
295. 50

295. 89

296. 22
295. 67
295. 65
295. 84
289. 45

295. 87

296. 61
295. 75
295. 49
295. 86
296. 17
295. 56
295. 48
295. 57
289. 34

0.908
2.286
3.798
5.871
8.633
12. 058
[16. 989]
21. 286
27. 162
16. 015

°C

9.96
24.99
35.00
45.00
54.99
64.96
74.94
85.03
95.30
74.94

°C
11.61

R

24.99

L

34.84

R

44.90

L

54.99

R

64. 79

L

76.30

R

85.03

L

95.92

L

74. 18

On calculating out the above data it was seen that the measure-
ment at 74. 94 was manifestly in error, hence the last observa-
tion in the table was made on the same solution two days later, it

82

Bulletin of the Bureau of Standards

Vol.14

having remained at room temperature in the meantime. The
temperatures in the last column were calculated by means of the
formula

T= (^ + 5)1.472 = ?-;*-■? + 58.62

It was easy to keep the solution at a temperature which was
constant within one-tenth of a degree, hence the formula does not
serve to reproduce the observed values satisfactorily. We may add
that in so viscous a solution the fluidity is greatly affected by the
temperature, a rise of i° at 45 causing an increase of 4.1 per
cent in the fluidity.

A 60 per cent solution was now prepared from commercial
sugar in order to learn whether an}- serious error would be made
in using commercial sugar instead of specially prepared sugar.
The solution proved to be 60.17 P er cen t sucrose. The fluidity
is given in Table 1 >•

TABLE 13

Fluidity of a 60.17 Per Cent Solution of Commercial Sugar at 74.94° C

1
Limb j Time, t

Pres-
sure, p

Pres-
sure, P

Fluidity,

Tem-
perature
observed

L

Seconds
1,484.6

292.91

292.80

16.08

°C
74.94

For convenience in comparison the observed fluidities were
plotted to a large scale and interpolated for even concentrations
and for every 5 . The resulting fluidities are given in Table 14
and the corresponding viscosities are given in Table 15.

TABLE 14

Fluidities of Sucrose Solutions Containing 0, 20, 40, and 60 Per Cent Sucrose by
Weight at Every 5° C (Interpolated)

Temper-

Percentage sucrose by weight

Temper-
ature, "C

Percentage sucrose by weight

ature, °C

1
0a 20

40

.

20

40

60

5 .

10

15

20

25

30

55.91
65.99
76.56
87.67
99.54
111.84
124. 70

26.29
31.71
37.71
44.11
51.02
58.69
66.51
75.12
83.82
93.42
103. 07

6.77
8.65
10.21
13.39
16.13
19.28
22.82
26.58
30.78
35.13
40.05

0.42
.64
.91
1.34
1.77
2.28
2.96
3.77
4.70
5.82
7.14

•

60

65

70

75

80

i 85

90

i 100

197. 16
212. 72
229. 41
246.18
263.57
281.21
299.31
317. 87
335.46
354. 49

113. 12
123. 79
134.81
145. 97
157. 56
169. 53
181.80

45.06
50.47
56.24
62.17
68.41
74.96
81.92
89.06
96.41
104.11

8.57
10.17
11.99
13.98
16.12
13.51
21.14

35

■\\<* 70

24.07

40 l«a r>7

26.85

4 5

167. 84
181.92

29.96

50

a These are the average fluidities calculated from Table 5.

Bingkaml
Jackson J

Viscosity Standards

83

TABLE 15

Viscosities in Centipoises of Sucrose Solutions Containing 0, 20, 40, and 60 Per Cent
Sucrose *by Weight at Every 5° C (Interpolated)

Temper-

Percentage sucrose by weight

Temper-
ature, °C

Percentage sucrose by weight

ature, °C

0«

20

40

60

20

40

60

5

10

15

20

25

30

35

1.789
1.516
1.306
1.141
1.005
.894
.802
.720
.653
.596
.550

3.804
3.154
2.652
2.267
1.960
1.704
1.504
1.331
1.193
1.070
.970

14.77
11.56
9.794
7.468
6.200
5.187
4.382
3.762
3.249
2.847
2.497

238

156

109.8
74.6
56.5
43.86
33. 78
26.52
21.28
17. 18
14.01

55.......

60

65

70

75

80

85

90

95

100

0.507
.470
.436
.406

.379
.356
.334
.315
.298
.282

0.884
.808

.742
.685
.635
.590
.550

2.219
1.982
1.778
1.608
1.462
1.334
1.221
1.123
1.037
.960

11.67
9.83
8.34
7.15
6.20
5.40
4.73
4.15

40

3.72

45

3.34

50........

o These are the average viscosities given in Table 5.

We reproduce here for the sake of comparison the viscosities of
sugar solutions obtained by Hosking, 26 Table 16, and by Powell, 27
Table 17. Burkhardt, 28 Rudorf, 29 Griineisen, 30 and Green 31 have
studied the viscosity of sugar solutions, but not over a range of
temperatures. The viscosities determined by Hosking are gen-
erally considerably lower than our values, although it is to be
noted that we agree with Hosking satisfactorily at the lowest
temperature in the 40 per cent solution and at the highest tempera-
ture in the 20 per cent solution. The values of Powell, are, in
general, intermediate between Hosking's values and our own, but
agree better with the former. Bingham, Schlesinger, and Coleman
obtained 1.731 cp for the viscosity of a 20 per cent sugar solution
at 2 5 C using the Washburn viscometer. This is considerably
higher than the present value.

26 Phil. Mag. [5], 49, p. 274; 1900.

27 Trans. (London) Chem. Soc, 105, p. 1; 1914.

28 Zs. Rubenzuckerind. 1874. Cf. Castell- Evans Physieo-Chemical Tables, 2, p. 652; 1911,

29 Zs. physik. Chem., 43, p. 281; 1903.

30 Wiss. Abh. d. Phys.-Tech. Reichsanstalt, 4, p. 239; 1905.

31 Trans. (I,ondon) Chem. Soc., 93, p. 2023; 1908.

84 Bulletin of the Bureau of Standards

TABLE 16
Viscosity of Sucrose Solutions in Centipoises According to Hosking j:

V*. 14

Teaper*tur». * C

::

ft M

:. a

3.720

L729

2.050

3.042

: -l:

L754

2.578

L292

L518

2.212

L139

: v.\

L910

LOW

.901

1.041

L485

.Ml

.933

L319

.-::

.843

:.::■:

.663

.763

L059

.611

.699

.961

.SM

.540

.592

.799

.487

.;--

.676

.--■:

. I ■

.359

. --■

.586

:--

-:.

.349

. :. : ;

1.810

5 L537

L 331

15 ! L168

20 ' 1.031

25

30 812

35

40

609

50 555

55

60

65 438

75 387

8D 362

85 Ml

14.76
1L33
8.95
7.30
6.07
5.08

- ;::
L€a

1 m

2.728
2.410
1 M
L908

L553

L414
L ■

1.182
L093

TABLE 17

Viscositr r5 According tD Powell ■

—

-

;:

:-

-:

:

1.17
LOS

-

LOO L18
.90 L06

:::

L6i
1.43

L28

1.15

s:

35

40

45

5}

-
.67
.61

.::

.'■:

n

- ::

L83
L62

L44

2.08

Same Solutions at 20 : According to Burkhardt

: .

:. :■■:: :.::: . :-:•- :-:: 2. :-:

From the data of Green 3 - we calculate the viscosity of a 40 per
cent solution to be 6.0S cp at 20° and 5.066 cp at :

We have not attempted to apply any corrections to the above
data, but the probable corrections would tend to decrease the

c Loc dt.

/ST] Viscosity Standards 85

viscosity, hence they would not help to bring about agreement
between our values and those of earlier observers.

In connection with the fact that our viscosities are in this case
higher than those of most of our predecessors, it is of interest to
note that when the viscosity of the commercial sugar solution used
by us was reduced to the basis of a 60 per cent solution at 75 ° C,
we obtain 6.07 cp, which is also lower than the 6.20 obtained by
us for specially purified sugar.

In the appendixes are given tables of densities of sucrose and
ethyl-alcohol solutions, reproduced here for the convenience of any
who may desire to use the data given in this paper for the purposes
of calibration.

VIII. SUMMARY

1. For the purpose of the calibration of viscometers, there is
need for one or more liquids whose viscosity is greater than that
of water, which can be easily obtained, and whose viscosity is
known with a considerable degree of certainty.

2. Of the suitable substances ethyl alcohol- water mixtures and
sucrose solutions each possess certain marked advantages. The
viscosities of the former are well known, there existing data by
several observers which agree as well as can be expected; but the
correctness of the data for the latter has been questioned. Hence
we have redetermined the viscosity of a 20 and a 40 per cent
solution by weight and have in addition measured the viscosity of
a 60 per cent solution from io° to 95 ° C. The viscosities obtained
by us are generally somewhat higher than the values obtained
hitherto, but we have every reason to believe that our values are
worthy of confidence.

3. The existing data on the viscosity of water has been reviewed
in order to correct it so far as possible according to our present
knowledge. The viscosity and fluidity of water for every degree
centigrade from o to 100 has been calculated.

absolute or specific units have been compared. The suggestion
has been made that by expressing all data in terms of the centi-
poise (the one-hundredth part of the cgs unit), the absolute vis-
cosity of substances would be practically also the specific viscosity,
provided that we take water at 20 as the standard. We find the
most probable value for the viscosity of water at 20 C to be
1.005 C P-

Washington, August 8, 191 6.

APPENDIXES

Appendix A. — Density in Grams per Milliliter of Mixtures of Ethyl Alcohol and Water

Per cent alcohol by weight 10° C 15° C

5
10
IS

n

25

90
35
40
IS

50

55

CO

f5

:o

"5
BO
85

90
95

IOC

0.99973
9098
8393
7800
7252
6665
5977
5162
4238
3226
2162
1055

.89927
8774
7602
6408
5197
3951
2654
1278

. 79784

0.99913
9032
8304
7669
7068
6424
5686
4832
3882
2852
1776
0659

. 89523
8364
7187
5988
4772
3525
2227
0852

. 79360

20° C

25° C

30° C

35° C |

0. 99823

0. 99708

0. 99568

0.99406

8938

8817

8670

8501

8187

8043

7875

7685

7514

7334

7133

6911

6864

6639

6395

6134

6168

5895

5607

5306

5382

5067

4741

4403

4494

4146

3790

3425

3518

3148

2770

2385

2472

2085

1692

1291

1384

0985

0580

0168

0258

. 89850

.89437

.89016

.89113

8699

8278

7851

7948

7527

7100

6667

6766

6340

5908

5470

5564

5134

4698

4257

4344

3911

3473

3029

3095

2660

2220

1774 :

1797

1362

0922

0478 |

0424

. 79991

. 79555

.79114 |

.78934

8506

8075

7641 ;

0.99225
8311
7475
6670
5856
4991
4055
3051
1992
0884
.89750

7417
6227
5025
3809
2578
1322
0028
78670
7203

33 This Bulletin, 9, p. 327; 1913.

Appendix B. — Density in Grams per Milliliter of Sucrose Solution

Per cent

sucrose by

weight

0°C

10° C

15° C

20° C

25° C

0. 99987

0. 99973

0.99913

0. 99S23

0. 99707

1. 02033

1. 01960

1.01884

1. 01784

1.C1661

4135

4016

3925

3813

3679

6304

6146

6041

5916

5772

8546

8353

8233

8094

7940

1. 10869

1. 10642

1. 10507

1. 10354

1. 10188

3274

3014

2863

2698

2517

5769

5473

5306

5127

4933

8349

8020

7837

7648

7439

1. 21018

1. 20657

1.20460

1. 20257

1. 20039

3775

3382

3173

2958

2732

6621

6203

5981

5753

5516

9560

9117

8884

8644

8399

1. 32591

1.32125

1. 31882

1.31631

1. 31376

5719

5230

4976

4716

4452

30° C

40° C

50° C

60° C

c

5
lfl

15

20
IS

9C
35
40
45
50
55
60
§5

70

0. 99567

1.01518
3530
5612
7767

1.10005
2324
4730
7214
9812

1.22495
5271
8144

1.31113
4181

0. 99232
1.01169

3165
5229
7366
9585

1. 11888

4279
6759
9332

1.21996
4756
7615

1.30571
3625

0. 98813

1. 00735

2720
4772
6898
9106 I

1. 11398 ,
3779 !
6248 j
8811 j

1.21465 i
4211 j
7058 j

1.30002 I
3047

0. 98330
1.00231

2198
4238
6358
8563

1.10850
3228
5693
8247

1.20891
3629
6468
9408

1. 32447

M Plato. Abh. Norm. Eich.-Komm., 2, p. 140. 1900; Zs. Zuckerindustrie. 50, pp. 982 and 1079, 1900; cf. Lan-
dolt and Bornstein's Physikalisch-Chemische Tabellcn, fourth ed., p. 311.

86

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